Local adjustment strategy-driven probabilistic linguistic group decision-making method and its application for fog-haze influence factors evaluation

Unlike other linguistic modellings, probabilistic linguistic term sets can express clearly the importance of different linguistic variables. The notion of Probabilistic Linguistic Preference Relations (PLPRs) constitutes an extension of linguistic preference relations, and as such has received increasing attention in recent years. In group decision-making (GDM) problems with PLPRs, the processes of consistency adjustment, consensus-achieving and desirable alternative selection play a key role in deriving the reliable GDM results. Therefore, this paper focuses on the construction of a GDM method for PLPRs with local adjustment strategy. First, we redefine the concepts of multiplicative consistency and consistency index for PLPRs, and some properties for multiplicative consistent PLPRs are studied. Then, in order to obtain the acceptable multiplicative consistent PLPRs, we propose a convergent consistency adjustment algorithm. Subsequently, a consensus-achieving method with PLPRs is constructed for reaching the consensus goal of experts. In both consistency adjustment process and consensusachieving method, the local adjustment strategy is utilized to retain the original evaluation information of experts as much as possible. Finally, a GDM method with PLPRs is investigated to determine the reliable ranking order of alternatives. In order to show the advantages of the developed GDM method with PLPRs, an illustration for determining the ranking of fog-haze influence factors is given, which is followed by the comparative analysis to clarify its validity and merits.